Inside/in/into are all fairly interchangeable, and refer to the interior. He went into the house/ he went inside the house, etc
On/onto usually refer to being on top of something, or being on the surface. He walked onto the roof, she stood on the bridge.
Cross is a rarely used abbreviation for across. Across refers to distances. He swam across the pool. They walked across the pier.
Round is a rarely used abbreviation for around. Around is a vague word that can imply a circular motion or a general direction. They walked around the puddle/ She walked around the park.
The different connotations of prepositions are confusing even to English speakers, so I wouldn't worry about it too much. Just know the general idea of the word and look at example sentences. Some English prepositions make no sense at all